With first-principles theoretical and symmetry analysis, we establish that (${\mathrm{PbMnO}}_3{)}_1$/(${\mathrm{PbVO}}_3{)}_1$ superlattice is a multiferroic with coexisting ferromagnetism, ferroelectricity, and Berry curvature dipole. Transfer of electronic charge from ${\mathrm{V}}^{4+}$ to ${\mathrm{Mn}}^{4+}$ is shown to drive (a) polar (${\mathrm{\Gamma }}_5^{-}$ symmetry) distortion dominated by ${\mathrm{V}}^{5+}$ ($d^0$) displacements, and (b) Jahn-Teller distortion of ${\mathrm{Mn}}^{3+}{\mathrm{O}}_6$ octahedra to open up a gap. Berry curvature and associated spin-polarized Berry curvature dipole are of magnitude comparable to that of Weyl semimetals composed of heavy elements with strong spin-orbit coupling. Integrating Berry curvature dipole with magnetoelectric multiferroic behavior of the heterostructure ${\mathrm{PbMnO}}_3$:${\mathrm{PbVO}}_3$ gives a combination of magnetoelectric coupling and electrically switchable anomalous Hall effects. The sign and spin-polarization of dc nonlinear transverse Hall voltage, generated by a longitudinal ac electric field, encodes nonvolatile four-state memory in a Hall device, making it useful for oxide electronics and spintronics.

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• Anomalous Hall effect
• Berry curvature
• Ferroelectricity
• Magnetic insulators
• Multiferroics
• Density functional theory
• First-principles calculations